Wilson loop and its correlators in the limit of large coupling constant

E Sysoeva

doi:10.1016/j.nuclphysb.2018.09.015

Abstract

In this paper we study Wilson loops in various representations for finite and large values of the color gauge group for supersymmetric N=4 gauge theories. We also compute correlators of Wilson loops in different representations and perform a check with the dual gravitational theory.

Highlights

3 we turn to the correlator of a symmetric Wilson loop with primary chiral operators, again both for finite and large N
Let us find a connected correlator between a WL in a symmetric representation and a chiral primary operator. This correlator can be written via matrix model integrals [5]
For a product of two symmetric Wilson loops one gets a sum of traces in the two-rows representations tr K⊗K′ eg a =

Summary

Wilson loops in arbitrary representations

Young-Mills theory with gauge group U (N ). We have e−a2u+g auKu. Thinking of a representation associated with a Young tableau with g+1 groups consisting of ni rows of the same length (including rows of zero length) one can notice that the integrand of (2.12) stays the same under the permutation u → σu such that Ku = Kσu. Thinking of a representation associated with a Young tableau with g+1 groups consisting of ni rows of the same length (including rows of zero length) one can notice that the integrand of (2.12) stays the same under the permutation u → σu such that Ku = Kσu It implies that the integral (2.12) over Ω can be replaced with the integral over the union of the images of Ω under all such permutations (let us denote it as Ω ) divided by the number of the permutations n1! In the following subsections we specify to some simple cases

The completely symmetric representation

Two-row Young tableau

Correlators of a symmetric Wilson loop and chiral primary operators

Correlators of two Wilson loops

Large N limit

String in degenerated genus one background